Again, it’s always been this way.
Managers are pressured to win. If analytics help them win, they want them.
The only change is what analytics are used. Baseball has been a stat driven sport for a long time now.
Even Earl Weaver, famous for his mantra of “pitching, defense, and three-run homers” used the available analytics. While Weaver tried to pass himself off as an “old school” fire and brimstone baseball guy, he was a complete slave to his available analytics. He employed position platoons more than any other contemporary manager, he used the a pitching rotation because the available data related pitcher rest to pitcher success (although he rebelled slightly with a 4 man rotation a lot) and he used lefty-righty bullpen matchups because data told him it worked. Weaver was also a front runner in de-emphasizing the importance of stolen bases.
Think Connie Mack did any of that? (Mack once used Christy Mathewson and Joe McGinnity to start a combined 90 of his teams 139 games, and then used them a combined 10 more times in relief.)